Are you taking Highway 61? (cue Bob Dylan)
Doe's Eat Place in Greenville is pretty famous, though I've never been there. It's probably hard to get bad barbecue anywhere around there. Just stay away from the pickled eggs.
I once visited Windsor Ruins, between Port Gibson and Alcorn. There's also a town near Alcorn called Rodney. It was a port until the river changed direction and left it dry.
The Delta is a photographer's dream if you like to take pictures of old dilapidated stores and churches.
Somebody once told me that the significance of "going down to Rosedale" was that Clarksdale was in a dry county, but Rosedale wasn't. I make no claims about the accuracy of that statement.